13-6] VIBRATION AND SHOCK 703 



environment of vibration are generally useful in shock as well. When the 

 application of isolators is considered, on the other hand, shock and vibration 

 sometimes seem to give conflicting requirements. This topic will now be 

 treated briefly. Crede^ has stated, "Isolation of vibration or shock signifies 

 the temporary storage of energy, and its subsequent release ... in a diff^erent 

 time relation. Isolation is thus distinct from the absorption or dissipation 

 of energy. The eff'ectiveness of an isolator is sometimes enhanced by limited 

 dissipation of energy, but this is a secondary consideration in its function." 



To consider a simple application of vibration isolators, let Fig. 13-8 

 represent the response of one vibrational mode of a chassis or assembly 

 mounted upon isolators (assuming a geometrical arrangement which 

 decouples the rotational and translational modes). The figure shows that 

 the transmissibility of the system is less than unity for all frequencies 

 greater than 1.4 times the undamped natural frequency, and becomes very 

 small at high frequencies when damping rates are small. The isolators thus 

 protect the equipment from damaging forces which might be transmitted 

 through a rigid connection to the structure, provided that the natural 

 frequencies of the resulting spring-mass system (loosely called the isolator 

 natural frequency) are low compared with the environmental vibration 

 frequencies. The low natural frequency of such a system requires relatively 

 "soft" isolator springs, permitting large deflections. In compact aircraft 

 installations, it is often difficult to provide the required clearance between 

 isolated equipments and the structure. 



It is not necessary to isolate for all possible environmental frequencies, 

 if the equipment can withstand the transmitted vibrations at isolator 

 resonance. For this situation, the isolators are required to provide signifi- 

 cant protection only at the lowest resonant frequency of the equipment and 

 at all higher frequencies. A general rule that appears workable is that the 

 isolator natural frequency should be less than 40 per cent of the lowest 

 resonant frequency within the equipment. 



The function of a shock isolator is to reduce large acceleration loads by 

 increasing the time interval during which the change in velocity of the 

 protected equipment occurs. Looking at this in another way, it can be said 

 that shock isolators are required to protect the mounted equipment by 

 storing much of the energy that would be transmitted to the equipment in 

 a shock impulse. This energy is then supposed to be released in a form that 

 does not damage the mounted equipment. 



Now let Fig. 13-7 represent a body mounted on shock isolators of stiffness 

 K lb /ft. If the supporting structure undergoes a shock velocity change of 

 V ft /sec and damping is negligible, the maximum acceleration of the mass 

 Mis 



Xm - V^. (13-13) 



2Charles E. Crede, Vibration and Shock Isolation, John Wiley & Sons, Inc., New York, 1951. 



